In a conventional extension plug-in unit, which consists of a socket attached to a first cable and a plug attached to a second cable, both the socket and the plug have a generally cylindrical shape. This cylindrical shape presents several problems. First, the contacts of the plug and the socket must be located within a circular area normally in parallel with their attached cables. Since it is not desired to make the diameter of the cylinder inordinately large, in extension plug-in units for relatively high currents, e.g. about 100 A, the connections between the cables and the connectors of the plug and the socket must be executed in succession in the axial direction. This considerably increases the length of both the plug and the socket, making them awkward and heavy to handle. On the other hand, the cylindrical shape necessitates a considerable force for inserting the plug into the socket, on account of the size of the friction surface therebetween. Further, these surfaces will be quickly soiled and become dirty, which adds to the force required. Also locking the parts of the extension plug-in unit together is relatively difficult with such cylindrical sockets and plugs. Often sleeve-like parts applying threaded couplings or the like must be used to perform the locking; the parts are adapted to slide and turn about the cylindrical body of the plug and socket but are not slidable in the axial direction beyond their free ends. Also, such axially elongated extension plug-in units cannot be accommodated in a small space and can utilize only very reduced bending radiuses. A further problem with such axially connectable sockets and plugs is that reliable coupling of the contacts in a specific order is relatively difficult to achieve without further increasing the length of the socket and the plug. Neither are the conventional extension plug-in unit plugs or sockets suitable for branching a cable but can only be employed for cable extension.